Relevant bibliographies by topics / Infinitesimal quantitie

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Infinitesimal quantitie'

Author: Grafiati
Published: 9 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Infinitesimal quantitie.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Infinitesimal quantitie"

1

Kadianakis, Nikos, and Fotios I. Travlopanos. "Infinitesimally affine deformations of a hypersurface." Mathematics and Mechanics of Solids 23, no. 2 (December 21, 2016): 209–20. http://dx.doi.org/10.1177/1081286516680261.

Full text
Abstract:
Affine deformations serve as basic examples in the continuum mechanics of deformable three-dimensional bodies (usually referred to as homogeneous deformations). They preserve parallelism of straight lines, and are often used as an approximation to general deformations. However, when the deformable body is a membrane, a shell or an interface modeled by a surface, parallelism is defined by the affine connection of this surface. In this work we study the infinitesimally affine time-dependent deformations (motions) of such a continuum, but in a more general context, by considering that it is modeled by a Riemannian hypersurface. First we prove certain equivalent formulas for the variation of the connection of the hypersurface. Some of these formulas are expressed in terms of geometrical quantities, and others in terms of kinematical quantities of the deforming continuum. The latter is achieved by using an adapted version of the polar decomposition theorem, frequently used in continuum mechanics to analyze motion. We also apply our results to special motions like tangential and normal motions. Further, we find necessary and sufficient conditions for this variation to be zero (infinitesimal affine motions), providing insight on the form of these motions and the kind of hypersurfaces that allow such motions. Finally, we give some specific examples of mechanical interest which demonstrate motions that are infinitesimally affine but not infinitesimally isometric.
APA, Harvard, Vancouver, ISO, and other styles
2

Fredericks, E., F. M. Mahomed, and K. Masike. "Lie Infinitesimal Conserved Quantities for Itô Stochastic ODEs." Mathematical and Computational Applications 15, no. 4 (December 1, 2010): 601–12. http://dx.doi.org/10.3390/mca15040601.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Ely, Robert. "Nonstandard Student Conceptions About Infinitesimals." Journal for Research in Mathematics Education 41, no. 2 (March 2010): 117–46. http://dx.doi.org/10.5951/jresematheduc.41.2.0117.

Full text
Abstract:
This is a case study of an undergraduate calculus student's nonstandard conceptions of the real number line. Interviews with the student reveal robust conceptions of the real number line that include infinitesimal and infinite quantities and distances. Similarities between these conceptions and those of G. W. Leibniz are discussed and illuminated by the formalization of infinitesimals in A. Robinson's nonstandard analysis. These similarities suggest that these student conceptions are not mere misconceptions, but are nonstandard conceptions, pieces of knowledge that could be built into a system of real numbers proven to be as mathematically consistent and powerful as the standard system. This provides a new perspective on students' “struggles” with the real numbers, and adds to the discussion about the relationship between student conceptions and historical conceptions by focusing on mechanisms for maintaining cognitive and mathematical consistency.
APA, Harvard, Vancouver, ISO, and other styles
4

Parameswaran, Revathy. "On Understanding the Notion of Limits and Infinitesimal Quantities." International Journal of Science and Mathematics Education 5, no. 2 (November 25, 2006): 193–216. http://dx.doi.org/10.1007/s10763-006-9050-y.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Shalyt-Margolin, A. E. "Minimal Length and the Existence of Some Infinitesimal Quantities in Quantum Theory and Gravity." Advances in High Energy Physics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/195157.

Full text
Abstract:
It is demonstrated that provided a theory involves a minimal length, this theory must be free from such infinitesimal quantities as infinitely small variations in surface of the holographic screen, its volume, and entropy. The corresponding infinitesimal quantities in this case must be replaced by the “minimal variations possible”—finite quantities dependent on the existent energies. As a result, the initial low-energy theory (quantum theory or general relativity) inevitably must be replaced by a minimal length theory that gives very close results but operates with absolutely other mathematical apparatus.
APA, Harvard, Vancouver, ISO, and other styles
6

Basu, Sanjib, Sreenivasa Rao Jammalamadaka, and Wei Liu. "Stability and infinitesimal robustness of posterior distributions and posterior quantities." Journal of Statistical Planning and Inference 71, no. 1-2 (August 1998): 151–62. http://dx.doi.org/10.1016/s0378-3758(98)00090-1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Urabe, M. "Assessment of tableting properties using infinitesimal quantities of powdered medicine." International Journal of Pharmaceutics 263, no. 1-2 (September 16, 2003): 183–87. http://dx.doi.org/10.1016/s0378-5173(03)00340-5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Cai, J. L., and F. X. Mei. "Conformal Invariance and Conserved Quantity of the Higher-Order Holonomic Systems by Lie Point Transformation." Journal of Mechanics 28, no. 3 (August 9, 2012): 589–96. http://dx.doi.org/10.1017/jmech.2012.67.

Full text
Abstract:
AbstractIn this paper, the conformal invariance and conserved quantities for higher-order holonomic systems are studied. Firstly, by establishing the differential equation of motion for the systems and introducing a one-parameter infinitesimal transformation group together with its infinitesimal generator vector, the determining equation of conformal invariance for the systems are provided, and the conformal factors expression are deduced. Secondly, the relation between conformal invariance and the Lie symmetry by the infinitesimal one-parameter point transformation group for the higher-order holonomic systems are deduced. Thirdly, the conserved quantities of the systems are derived using the structure equation satisfied by the gauge function. Lastly, an example of a higher-order holonomic mechanical system is discussed to illustrate these results.
APA, Harvard, Vancouver, ISO, and other styles
9

Paganelli, Simone, and Tony J. G. Apollaro. "Irreversible work versus fidelity susceptibility for infinitesimal quenches." International Journal of Modern Physics B 31, no. 06 (March 5, 2017): 1750065. http://dx.doi.org/10.1142/s0217979217500655.

Full text
Abstract:
We compare the irreversible work produced in an infinitesimal sudden quench of a quantum system at zero temperature with its ground state fidelity susceptibility, giving an explicit relation between the two quantities. We find that the former is proportional to the latter but for an extra term appearing in the irreversible work which includes also contributions from the excited states. We calculate explicitly the two quantities in the case of the quantum Ising chain, showing that at criticality they exhibit different scaling behaviors. The irreversible work, rescaled by square of the quench’s amplitude, exhibits a divergence slower than that of the fidelity susceptibility. As a consequence, the two quantities obey also different finite-size scaling relations.
APA, Harvard, Vancouver, ISO, and other styles
10

Urabe, M., S. Ito, S. Itai, and H. Yuasa. "Assessment of tableting properties using infinitesimal quantities of powder medicine II." Journal of Drug Delivery Science and Technology 16, no. 5 (2006): 357–61. http://dx.doi.org/10.1016/s1773-2247(06)50065-6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Infinitesimal quantitie"

1

BARACCO, FLAVIO. "HERMANN WEYL AND HIS PHENOMENOLOGICAL RESEARCHES WITHIN INFINITESIMAL GEOMETRY." Doctoral thesis, Università degli Studi di Milano, 2019. http://hdl.handle.net/2434/638166.

Full text
Abstract:
The present work focuses on the mathematical and philosophical works of Hermann Weyl (1885-1955). Weyl was a leading mathematician at the beginning of the twentieth century and his major contributions have concerned several fields of research, both within pure mathematics and theoretical physics. Many of them were pioneering works at that time and, most of all, they were carried out in the light of his peculiar philosophical view. As few mathematicians of his time, Weyl was able to manage both scientific and philosophical issues with an impressive competence. For this reason he represented a very peculiar figure among scientists and mathematicians of his time. This dissertation aims to clarify these works both from a philosophical and a mathematical perspective. Specifically, I will focus on those works developed through the years 1917-1927. The first chapter aims to shed some light on the philosophical reasons that underlie Weyl's foundational studies during this period. I will explore these works especially with respect his attempt to establish a connection between a descriptive analysis of phenomena and their exact determination. I will focus both on his mathematical formulation of Euclidean space and on his analysis of phenomenal continuum pointing out the main features of these studies. Weyl's investigations on the relations between what is intuitively given and the mathematical concepts through which we seek to construct the given in geometry and physics do not seem to be carried out by chance. These investigations indeed could be better understood within the phenomenological framework of Husserl's philosophy. Husserl's distinction between descriptive and exact concepts delineates the difference between a descriptive analysis of a field of inquiry and its exact determination. Clarifying how they are related is not an easy task. Nevertheless, Husserl points out that a connection might be possible if we were able to establish a connection by means of some idealizing procedure intuitively ascertained. Within this phenomenological framework we should interpret Weyl's investigations on the relation between phenomenal knowledge and theoretical construction. In the second chapter I will focus on Weyl's mathematical account of the continuum within the framework of his pure infinitesimal geometry developed mainly in \emph{Raum-Zeit-Materie}. It deserves a special attention. Weyl indeed seems to make use of infinitesimal quantities and this fact appears to be rather odd at that time. The literature on this issue is rather poor. For this reason I've tried to clarify Weyl's use of infinitesimal quantities considering also Weyl's historical context. I will show that Weyl's approach has not to be understood in the light of modern differential geometry. It has instead to be understood as a sort of algebraic reasoning with infinitesimal quantities. This approach was not so unusual at that time. Many mathematicians, well-known to Weyl, were dealing with kind of mathematics although many of these studies were works in progress. In agreement with that, Weyl's analysis of the continuum has to be understood as a work in progress as well. In the following Weyl's studies in combinatorial topology are proposed. I will then suggest that both these approaches should be understood within the phenomenological framework outlined in the first chapter. The latter, however, attempts to establish a more faithful connection between a descriptive analysis of the continuum and its exact determination and for this reason it can be regarded as an improvement with respect to the former from a phenomenological point of view. Finally, in the third chapter I will attempt a phenomenological clarification of Weyl's view. In the first and second chapter Weyl's studies are clarified showing how they are related with the phenomenological framework of Husserl's philosophy. Despite this, the theoretical proposal revealed by them is not so easy to understand. That issue seems to be shared by many other contemporary studies. The relevant literature on this author dealing with a phenomenological interpretation seems often to be hardly understandable. I'm going to outline the main problems involved in this field of research and how they are related with the peculiarity of Husserl's framework. I will then suggest a way to improve these studies. Specifically, I will attempt a phenomenological clarification of Weyl's writings. To this aim, I will argue for an approach that makes use of Husserl's writings as a sort of ``analytic tools'' so that a sort of phenomenologically-informed reconstruction of Weyl's thought can be achieved. I will finally consider Weyl's notion of surface as a case study to show a concrete example of this kind of reconstruction.
APA, Harvard, Vancouver, ISO, and other styles

Books on the topic "Infinitesimal quantitie"

1

Button, Tim, and Sean Walsh. Compactness, infinitesimals, and the reals. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0004.

Full text
Abstract:
One of the most famous philosophical applications of model theory is Robinson’s attempt to salvage infinitesimals. Infinitesimals are quantities whose absolute value is smaller than that of any given positive real number. Robinson used his non-standard analysis to formalize and vindicate the Leibnizian approach to the calculus. Against this, the historian Bos has questioned whether the infinitesimals of Robinson's non-standard analysis have the same structure as those of Leibniz. We offer a response to Bos, by building valuations into Robinson's non-standard analysis. This chapter also introduces some related discussions of independent interest (compactness, instrumentalism, and o-minimality) and contains a proof of The Compactness Theorem and Gödel’s Completeness Theorem.
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Infinitesimal quantitie"

1

Benferhat, Salem. "Infinitesimal Theories of Uncertainty for Plausible Reasoning." In Quantified Representation of Uncertainty and Imprecision, 303–56. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-1735-9_10.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Fiaschi, Lorenzo, and Marco Cococcioni. "Generalizing Pure and Impure Iterated Prisoner’s Dilemmas to the Case of Infinite and Infinitesimal Quantities." In Lecture Notes in Computer Science, 370–77. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40616-5_32.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Levey, Samuel. "The Continuum, the Infinitely Small, and the Law of Continuity in Leibniz." In The History of Continua, 123–57. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198809647.003.0007.

Full text
Abstract:
This chapter studies Leibniz’s watershed contributions to the analysis of continuity. Special attention is given to two early texts, Pacidius Philalethi and De Quadratura Arithmetica (both 1676), that document his central views on the composition of the continuum and the foundations of his infinitesimal geometry (and, later, his infinitesimal calculus); and to a handful of later documents, notably Specimen geometriae luciferae (1695) and Cum prodiisset (c. 1701), which reveal Leibniz’s groundbreaking new analysis of the concept of continuity of space, his definition of continuity for functions, and his most considered defense of the use of infinitesimals in his calculus as fictions. Leibniz holds that real quantities in nature are always actually infinitely divided into parts but never into points or infinitesimals. Contrary to popular history, Leibniz’s calculus is not committed to infinitesimals but is developed in strict accord with the axiom of Archimedes and the related principle that quantities that differ by less than any given quantity are equal.
APA, Harvard, Vancouver, ISO, and other styles
4

"Generality and Infinitely Small Quantities in Leibniz’s Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves." In Infinitesimal Differences, edited by Ursula Goldenbaum and Douglas Jesseph. Berlin, New York: Walter de Gruyter, 2008. http://dx.doi.org/10.1515/9783110211863.171.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Stewart, Ian. "4. The flipside of infinity." In Infinity: A Very Short Introduction, 54–69. Oxford University Press, 2017. http://dx.doi.org/10.1093/actrade/9780198755234.003.0005.

Full text
Abstract:
‘The flipside of infinity’ examines a logical counterpart of the infinite: infinitesimals. These are quantities that are infinitely small, instead of infinitely large. Historically, such quantities formed the basis of calculus, one of the most useful branches of mathematics ever invented. However, they caused considerable head-scratching, starting an argument that took about two centuries to resolve. This was achieved using a version of Aristotle’s potential infinity—namely, potential infinitesimality. Exhaustion is also explained, along with the modern concept of a limit, which abolished infinitesimals. Then it considers how infinitesimals were reinstated and outlines non-standard analysis, which provides a logical framework for infinitesimals.
APA, Harvard, Vancouver, ISO, and other styles
6

F. Crosta, Giovanni, and Goong Chen. "Transformation Groups of the Doubly-Fed Induction Machine." In Matrix Theory - Classics and Advances [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.102869.

Full text
Abstract:
Three-phase, doubly-fed induction (DFI) machines are key constituents in energy conversion processes. An ideal DFI machine is modeled by inductance matrices that relate electric and magnetic quantities. This work focuses on the algebraic properties of the mutual (rotor-to-stator) inductance matrix Lsr: its kernel, range, and left zero divisors are determined. A formula for the differentiation of Lsr with respect to the rotor angle θr is obtained. Under suitable hypotheses Lsr and its derivative are shown to admit an exponential representation. A recurrent formula for the powers of the corresponding infinitesimal generator A0 is provided. Historically, magnetic decoupling and other requirements led to the Blondel-Park transformation which, by mapping electric quantities to a suitable reference frame, simplifies the DGI machine equations. Herewith the transformation in exponential form is axiomatically derived and the infinitesimal generator is related to A0. Accordingly, a formula for the product of matrices is derived which simplifies the proof of the Electric Torque Theorem. The latter is framed in a Legendre transform context. Finally, a simple, “realistic” machine model is outlined, where the three-fold rotor symmetry is broken: a few properties of the resulting mutual inductance matrix are derived.
APA, Harvard, Vancouver, ISO, and other styles
7

Swendsen, Robert H. "Perturbations of Thermodynamic State Functions." In An Introduction to Statistical Mechanics and Thermodynamics, 124–31. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198853237.003.0010.

Full text
Abstract:
Because small changes in thermodynamic quantities will play a central role in much of the development of thermodynamics, the key concepts are introduced in this short chapter. The First Law (conservation of energy) can be expressed simply in terms of infinitesimal quantities: a small change in the energy of a system is equal to the heat added plus the work done on the system. The theories of statistical mechanics and thermodynamics deal with the same physical phenomena. Exact and inexact differentials are defined, along with the important concept of an integrating factor that relates them. The useful equation relating small changes in heat to corresponding changes in entropy is derived.
APA, Harvard, Vancouver, ISO, and other styles
8

Binney, James. "1. Big ideas." In Astrophysics: A Very Short Introduction, 1–10. Oxford University Press, 2016. http://dx.doi.org/10.1093/actrade/9780198752851.003.0001.

Full text
Abstract:
Isaac Newton laid the foundations of astrophysics when he showed that it is possible to obtain precise quantitative predictions from appropriately defined physical laws. To do this, he had to invent new mathematics—the infinitesimal calculus—and use its language to encapsulate physical laws. Astrophysics is the application of the laws of physics to everything that lies outside our planet. ‘Big ideas’ outlines the differential equations that make up these physical laws and explains that they are valid in every part of the universe and at all time. The universal and eternal nature of the laws of physics gives rise to three important conserved quantities: momentum, angular momentum, and energy.
APA, Harvard, Vancouver, ISO, and other styles
9

Mazur, Joseph. "The Last of the Magicians." In Enlightening Symbols. Princeton University Press, 2016. http://dx.doi.org/10.23943/princeton/9780691173375.003.0019.

Full text
Abstract:
This chapter discusses Isaac Newton's contributions to algebra and mathematics, and particularly in terms of using symbols. It first examines Newton's idea of unknown variables as quantities flowing along a curve. Fluents, as he called them (from the Latin fluxus, which means “fluid”), were very close to the things that we now call dependent variables, our x's, but limited by their dependence on time. Newton thought of curves as “flows of points” that represented quantities. According to Newton, the fundamental task of calculus was to find the fluxions of given fluents and the fluents of given fluxions. The chapter also considers Newton's work on infinitesimals and how his invention of calculus advanced a wide range of fields such as architecture, astronomy, chemistry, optics, and thermodynamics. It also describes some of the major developments that occurred in the fifty years following Newton's death.
APA, Harvard, Vancouver, ISO, and other styles
10

Handelman, Matthew. "Infinitesimal Calculus: Subjectivity, Motion, and Franz Rosenzweig’s Messianism." In The Mathematical Imagination, 104–44. Fordham University Press, 2019. http://dx.doi.org/10.5422/fordham/9780823283835.003.0004.

Full text
Abstract:
By way of Leibniz’s and Newton’s calculi and Hermann Cohen’s neo-Kantianism, Chapter 3 explores how infinitesimal calculus allowed Franz Rosenzweig to embed messianism into the daily work of thought. Through metaphors of space and subjectivity, the idea of the differential—the infinitely small quantity—synthesized the finitude of lived experience with the infinitude of the Absolute. In Rosenzweig’s The Star of Redemption (1921), the differential revealed a world in which the thinking individual works toward the redemption of the world, thus arguing for the modern relevance of Judaism despite the apparent world-historical hegemony of Christianity. For Rosenzweig, the differential pointed to a “messianic theory of knowledge,” which made room for the truths verified by belief alongside those proved by mathematics. It also underscored the epistemological significance of marginalized beliefs and experiences—even of those people who stand on the sidelines of so-called world history—in the project of redemption.
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Infinitesimal quantitie"

1

Taves, Jay, Alexandra Kissel, and Dan Negrut. "Dwelling on the Connection Between SO(3) and Rotation Matrices in Rigid Multibody Dynamics – Part 1: Description of an Index-3 DAE Solution Approach." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-72057.

Full text
Abstract:
Abstract In rigid multibody dynamics simulation using absolute coordinates, a choice must be made in relation to how to keep track of the attitude of a body in 3D motion. The commonly used choices of Euler angles and Euler parameters each have drawbacks, e.g., singularities, and carrying along extra normalization constraint equations, respectively. This contribution revisits an approach that works directly with the orientation matrix and thus eschews the need for generalized coordinates used at each time step to produce the orientation matrix A. The approach is informed by the fact that rotation matrices belong to the SO(3) Lie matrix group. The numerical solution of the dynamics problem is anchored by an implicit first order integration method that discretizes, without index reduction, the index 3 Differential Algebraic Equations (DAEs) of multibody dynamics. The approach handles closed loops and arbitrary collections of joints. Our main contribution is the outlining of a systematic way for computing the first order variations of both the constraint equations and the reaction forces associated with arbitrary joints. These first order variations in turn anchor a Newton method that is used to solve both the Kinematics and Dynamics problems. The salient observation is that one can express the first order variation of kinematic quantities that enter the kinematic constraint equations, constraint forces, external forces, etc., in terms of Euler infinitesimal rotation vectors. This opens the door to a systematic approach to formulating a Newton method that provides at each iteration an orthonormal rotation matrix A. The Newton step calls for repeatedly solving linear systems of the form Gδ = e, yet evaluating the iteration matrix G and residuals e is inexpensive, to the point where in the Part 2 companion contribution the proposed formulation is shown to be two times faster for Kinematics and Dynamics analysis when compared to the Euler parameter and Euler angle approaches in conjunction with a set of four mechanisms.
APA, Harvard, Vancouver, ISO, and other styles
2

A. Scarth, Douglas, Joanna Wu, Ted Smith, and Dennis M. Kawa. "Development of Weight Functions for Modelling Delayed Hydride Cracking Initiation at a Blunt Flaw." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2302.

Full text
Abstract:
Delayed Hydride Cracking (DHC) in Zr-2.5 Nb alloy material is of interest to the CANDU (Canada Deuterium Uranium) industry in the context of the potential to initiate DHC at a blunt flaw in a CANDU reactor pressure tube. The material is susceptible to DHC when there is diffusion of hydrogen atoms to the flaw, precipitation of hydride platelets, and development of a hydrided region at the flaw tip. The hydrided region can then fracture to the extent that a crack forms, and is able to grow by the DHC crack growth mechanism. An engineering process-zone model for evaluation of DHC initiation at a blunt flaw that takes into account flaw geometry has been developed. The model is based on representing the stress relaxation due to hydride formation, and crack initiation, by an infinitesimally thin process zone. Application of the engineering process-zone model requires calculation of the stress intensity factor, and the crack-mouth opening displacement, for a fictitious crack at the tip of a blunt flaw. In the current model, calculation of these quantities is based on a cubic polynomial fit to represent the stress distribution ahead of the blunt flaw tip, where the stress distribution is generally calculated by finite element analysis. However, the cubic polynomial is not always an optimum fit to the stress distribution for very small root radius flaws, due to the large stress gradients near the flaw tip. Application of the weight function method will enable a more accurate representation of the flaw-tip stress distribution for the calculation of the stress intensity factor and the crack-mouth opening displacement. Weight functions for a crack at the tip of a blunt flaw in a thin wall cylinder have been developed for implementation into the engineering process-zone model. These weight functions are applicable to a wide range of blunt flaw depths and root radii, as well as a wide range of flaw-tip crack depths. The development and verification of the weight functions is described in this paper. The verification calculations are in reasonable agreement with alternate solutions, and have confirmed that the weight functions have reasonable accuracy for engineering applications of the process-zone methodology.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Infinitesimal quantitie' for particular source types:
Journal articles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography